Problem: Simplify the following expression: $t = \dfrac{-7a^2 + 28a + 35}{a - 5} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ t =\dfrac{-7(a^2 - 4a - 5)}{a - 5} $ Then we factor the remaining polynomial: $a^2 {-4}a {-5} $ ${-5} + {1} = {-4}$ ${-5} \times {1} = {-5}$ $ (a {-5}) (a + {1}) $ This gives us a factored expression: $\dfrac{-7(a {-5}) (a + {1})}{a - 5}$ We can divide the numerator and denominator by $(a + 5)$ on condition that $a \neq 5$ Therefore $t = -7(a + 1); a \neq 5$